congrats on winning the battle!
curious as to how you hook up the hose while on the trailer....??? how did you winterize the engine with the failed pump???
with raw water cooled sterndrives, running on the hose, it is not unusual to be able to feel the temp change as the thermostat opens and closes....
is the strainer cap on tight, with a good gasket??? all the raw water hose clamps tight?
do you have access to some 1.25" ID clear vinyl tube?? can be useful for temporary use in troubleshooting cooling issues?
finally, is the oil level ok and the oil 'normal' in color?